The main reasons causing the transformer tank vibration are vibration from the transformer body and cooling system installations. The fundamental vibration frequency caused by the cooling device is low, and is significantly different to from the transformer body vibration; transformer body vibration includes core and winding vibration. During operation, the current in windings produces electromagnetic field in both core and winding; core silicon steel materials in the magnetic field have magnetostriction, namely the size of the atom has a small deformation, causing the core vibration. The solid line in FIG. 1 describes the relationship between the magnetostrictive deformation and core flux density. To simplify, use the quadratic curve, namely the dashed line. It can be seen that the magnetostrictive deformation is a linear relationship with the square of the size of the magnetic flux density. The relationship between the load voltage and magnetic flux density is:
  B  =            Φ      A        =                            2                ⁢        U                    2        ⁢        π        ⁢                                  ⁢        fNA            
Where ψ and B are main flux and magnetic flux density, respectively; A is cross-sectional area of the core; U is load voltage; f is the frequency of load voltage; N is the number of turns of primary winding.
In FIG. 1, core vibration vcore caused by the magnetostriction is approximately proportional to the square of load voltage:vcore∝U2;
As the duplation frequency of voltage is 100 Hz, the fundamental frequency of magnetostriction is 100 Hz.
Core is made from silicon steel, each piece of silicon steel surface is insulating coated, so there is a gap between segments, resulting in magnetic flux leakage, cause core and tank vibration. But the vibration can be ignored because it is much smaller than the vibration caused by magnetostriction. So the core vibration depends on the magnetostriction of silicon steel, the core vibration fundamental frequency is 100 Hz. Because of the nonlinear magnetostrictive and different magnetic circuit length of core inside and outside the box, the core vibration, in addition to the fundamental frequency, also contains the harmonic components, which are integer multiple of the fundamental frequency component.
The vibration of the winding is caused by electric power. Under the influence of the leakage inductance, current in winding interacts to generate electric force, which is proportional to the square of the current. Winding current is zero on no-load condition, so winding vibration now has no influence on core vibration. The vibration of the no-load transformer depends on the core.
According to above analysis, no-load tank vibration is related to core magnetostriction, namely related to voltage. Transformer vibration transmits to tank via transformer oil and solid structures. Be influenced by various factors, vibration signal changes in amplitude and phase. When it reaches the tank surface, it becomes complex.
After the loosening of the core, the magnetic flux leakage between the silicon steel joints and laminations become larger, resulting in larger electromagnetic attractive force, larger core vibration.
The transformer vibration signal is non-stationary signals. Signal processing methods include Fourier transform, wavelet transform, Hilbert Huang Transform. The Fourier transform is the most classic signal processing methods. It is suitable for stationary signals, to transform time domain of the signals to frequency domain, is widely used in engineering. Wavelet de-noising principle is shown in FIG. 2, the high-frequency signal can be filtered by the signal decomposition and reconstruction, reorganize low-frequency signal to the filtering effect.